You need to build the wall of a joist and preferable you need to add an additional joist and bolt it to the existing.
The floor boards are not designed to take the partition load and a signle joist could cause the wall to crack specially if it is plastered.

1. On top of boards. As the stud will not be load bearing no additional support should be needed so put it where you want it. This is because if the stud is parallel to the joists then it will be a right angles to the floorboards. If its parallel to the boards then it will be at right angles to the joists. So whatever you do it will be supported.

2. If you are going to tile the floor do not put floorboards down in the ensuite. Use 25mm WBP ply and ensure that all edges are screwed down at 100 - 150 mm centres. Put in extra noggins if necessary to achieve this and you wil have a very firm substrate for tiling.